We're building a course for our employees. It should be entirely self-guided and automated (we won't be marking anything or interacting with students in any way - once the course is set up, it just exists for people to learn from on their own).

I have an activity where I want students to write an answer to a question (1-4 sentences) and submit it. Then I want Moodle to show their answer beside our model answer/marking guide for that question so they can check their own work. How can I do this?

I tried the essay question format but that requires that a teacher formally grade it.

I tried short answer but that requires that the student type word for word what the correct answer is.

And it seems neither essay nor short answer allows the student to see their own answer after it has been submitted.

Any suggestions? I'm stumped by how such a simple thing seems so complicated!

If I correctly understand what you want, you CAN do it with a a quiz essay type question. The trick is to make sure you use any Question behavior EXCEPT for one of the Deferred feedback options, so that Review options > During the attempt is enabled and that you have checks for everything except Overall feedback.

Type your model response and marking guide info into the General feedback area of the essay question, when you create the essay question.

When the student finishes and submits the quiz, they will see their response and right underneath it, the General feedback. Even after they finish the review, they can come back and look again later. If they are allowed to take the quiz multiple time, each one of the attempts will be available for review. There NO need for a teacher to actually grade the essay question. Completion tracking can even be used, just do NOT use any one of the options that require a grade. Just simply set for Student must view this activity to complete it, will work.

I would suggest to go for workshop activity.
You can provide a model answer and ask the students to grade themselves depending on whether the student has given the answer close to the model answer.
Try it once and I am sure, you will love it.